Oscillation responses and wake modes of three staggered rotating cylinders, free to move in streamwise and transverse directions, are numerically studied in two- (2-D) and three-dimensional (3-D) flows. 2-D computations are carried out for Reynolds number Re = 60-150, employing the following rotation rates (α), respectively, for the upstream, upper, and lower downstream cylinders: 1, 1, 0; 1, 1, 1; 1, 1, −1. Here, the clockwise rotation is positive. 3-D simulations are performed at Re = 2000 and reduced velocity, U* = 2-11, with the three cylinders being rotated at α = 1. Bell-shaped amplitude profiles are observed for all the rotating cylinders, indicating that the bodies undergo vortex-induced vibrations. In 2-D flow, the considered Re regime can be categorized into three distinct regions, based on the oscillation and frequency responses. Cylinders exhibit negligible amplitudes in the first region, whereas the second region is characterized by high amplitude lock-in oscillations for all three cylinders. In the third region, the downstream cylinders exhibit lock-in response in certain rotation configurations. The oscillation responses and wake modes appear sensitive to the direction of rotation of the lower downstream cylinder for the streamwise and transverse gaps of 5 diameters (5D) and 3D, respectively, between the cylinders. Depending on the rotation configuration, 2S, P, and P + S modes of primary shedding are observed. In 3-D flow also, the cylinders exhibit bell-shaped amplitude profiles, contrary to the galloping response noticed for isolated rotating cylinders in few previous studies. Higher and lower amplitude oscillations induce stronger and weaker 3-D flow instabilities, respectively, in the wake region. © 2018 Author(s).